171. Ratio of milk to water in a mixture is 3:2. 30 Liters of mixture taken out and then 20 Liters of water is added in the mixture. Now the ratio of milk to water of the mixture is 3:7. If X% of the total initial mixture is 14, then find the value of X?

एक मिश्रण में दूध और पानी का अनुपात 3:2 है। 30 लीटर मिश्रण निकाला जाता है और फिर मिश्रण में 20 लीटर पानी मिलाया जाता है। अब मिश्रण के दूध और पानी का अनुपात 3:7 है। यदि कुल प्रारंभिक मिश्रण का X% 14 है, तो X का मान ज्ञात कीजिए?

A. 28
B. 15
C. 32
D. 36
E. 56

Option “A” is correct.

Let milk and water is 3a and a.

So, [3a-(30*3/5)]/[2a-(30*2/5)+20] = 3/7

3a-18/ (2a+8) =3/7

6a + 24 = 21a – 126

15a = 150

a = 10

Total mixture is 5*10=50

So, X% of 50 = 14, so X=14*100/50=28

172. In 165 litres mixture, the ratio of milk and water is 7:4. If X liters of the mixture taken out and 33 liters of milk is added to the remaining mixture, then the percentage of milk is 143.75% more than that of water. Then find the value of X.

165 लीटर मिश्रण में दूध और पानी का अनुपात 7:4 है। यदि X लीटर मिश्रण निकाला गया और शेष मिश्रण में 33 लीटर दूध मिला दिया जाता है, तो दूध का प्रतिशत पानी की तुलना में 143.75% अधिक है। तो X का मान ज्ञात कीजिए।

A. 32
B. 33
C. 35
D. 38
E. None of these

Option “B” is correct.

Quantity of milk = (7/11) * 165 = 105 liters

Quantity of water = (4/11) * 165 = 60 liters

ATQ, Ratio of milk and water in final mixture is, 39:16

Let removed quantity, X = 11x

(105 – 7x + 33)/ (60 – 4x) = 39/16

2208 – 112x = 2340 – 156x

44x = 132

Solve x = 3

X = 11 * 3 = 33 liters

173. Three liquids which are different percentage of milk as 15% of milk, 18% of milk and a% of milk are mixed in the ratio of their quantity 5:7: 9 respectively. If 17% of the milk is present in the final mixture. Then find what will be the value of a?

तीन तरल पदार्थ जिसमें दूध के 15%, दूध के 18% और दूध के a% के रूप में अलग-अलग प्रतिशत हैं, उन्हें क्रमशः 5:7:9 की मात्रा के अनुपात में मिलाया जाता है। यदि अंतिम मिश्रण में 17% दूध मौजूद है। तो ज्ञात कीजिए कि a का मान क्या होगा?

A. 12 (3/4)%
B. 17 (1/3)%
C. 15 (4/5)%
D. 16 (2/3) %
E. None of these

Option “B” is correct.

Let the quantity of three liquids are 500x, 700x and 900x respectively.

In first liquid, 15% of milk means = 75x milk

In second liquid, 18% of milk means = 126x milk

And, in third liquid, a% of milk means = 9ax milk

Then, according to the question,

(75x + 126x + 9ax)/(2100x) = 17/100

(201x + 9ax)/(2100x) = 17/100

a = (357x – 201x)/9x

a = 17 (1/3)%

Hence, the required answer = 17 (1/3)%.

174. In a mixture of milk and water, the quantity of milk is (x+40) and water 40 L. If 20 L milk and 8 L water is added to the mixture,then the ratio of milk and water becomes 5:3. Find the x% of initial water in the mixture?

दूध और पानी के मिश्रण में दूध की मात्रा (x+40) और पानी 40L है। यदि मिश्रण में 20L दूध और 8L पानी मिला दिया जाए, तो दूध और पानी का अनुपात 5:3 हो जाता है। मिश्रण में प्रारंभिक पानी का x% ज्ञात कीजिए?

A. 7L
B. 5L
C. 12L
D. 16L
E. None of these

Option “E” is correct.

So, we can say, [x+40+20]/(40+8) = 5/3

Or, 3x+180=48*5=240

Or, 3x=60, or, x=60/3=20

Required value is = 40*20/100=8 L

175. A vessel contains 60% of the milk and rest is water. 80 liters of the mixture is removed from the vessel and x liters of water is added, then the ratio of milk to water is 6:5. Find the value of x, if the difference between the initial quantity of milk and water is 40 liters?

एक बर्तन में 60% दूध है और शेष पानी है। बर्तन से 80 लीटर मिश्रण निकाल दिया जाता है और उसमें x लीटर पानी मिला दिया जाता है, तो दूध से पानी का अनुपात 6:5 हो जाता है। x का मान ज्ञात कीजिए, यदि दूध और पानी की प्रारंभिक मात्रा का अंतर 40 लीटर है?

A. 12
B. 18
C. 20
D. 15
E. None of these

Option “A” is correct.

Ratio of initial quantity of milk to water = 3:2

Initial quantity of milk = 40 * 3 = 120 liters

Initial quantity of water = 40 * 2 = 80 liters

 (120 – 80 * 3/5)/(80 – 80 * 2/5 + x) = 6/5

(120 – 48)/(80 – 32 + x) = 6/5

72/(48 + x) = 6/5

360 = 288 + 6x

6x = 72

x = 12 liters

176. In the first mixture, the quantity of milk was (x+10) liters and the quantity of water was x liters. If after adding 75 liters of the second mixture which has the milk and water is in the ratio of 13:2 into the first mixture, then the ratio of milk to water in the final mixture is 16:3. Find the value of x.

पहले मिश्रण में दूध की मात्रा (x+10) लीटर और पानी की मात्रा x लीटर थी। यदि 75 लीटर दूसरे मिश्रण को जिसमें दूध और पानी 13:2 के अनुपात में है, पहले मिश्रण में मिलाने के बाद, तो अंतिम मिश्रण में दूध से पानी का अनुपात 16:3 है। x का मान ज्ञात करें।

A. 6
B. 7
C. 4
D. 5
E. None of the above

Option “D” is correct.

In the second mixture, the ratio of milk and water is 13:2 respectively.

Milk =75*13/15 =65 liters

Water = 10 liters

(x+10+65)/(x+10) =16/3

(x+75)/(x+10) =16/3

3x+225 = 16x+160

13x=65

x=5

177. A vessel contains 540 liters mixture of milk and water and it contains 55(5/9)% of milk. If x liters of milk is added to the mixture, then the ratio of milk to water in the final mixture becomes 3:1, find the value of x?

एक बर्तन में 540 लीटर दूध और पानी का मिश्रण है और इसमें 55 (5/9)% दूध है। यदि मिश्रण में x लीटर दूध मिलाया जाता है, तो अंतिम मिश्रण में दूध से पानी का अनुपात 3:1 हो जाता है, x का मान ज्ञात कीजिए?

A. 420
B. 120
C. 280
D. 250
E. None of these

Option “A” is correct.

Initial quantity of milk in the vessel = 5/9 * 540 = 300 liters

Initial quantity of water in the vessel = 540 – 300 = 240 liters

(300 + x) / 240 = 3/1

x = 720 – 300

x =420

178. 300 gram mixture of turmeric and chili powder contains 36% of chili power. If x gram of turmeric powder added into the mixture, so that the quantity of turmeric powder in the resultant mixture becomes 80%, find the value of x?

300 ग्राम हल्दी और मिर्च पाउडर के मिश्रण में 36% मिर्च पाउडर होता है। यदि मिश्रण में x ग्राम हल्दी पाउडर मिलाया जाता है, ताकि परिणामी मिश्रण में हल्दी पाउडर की मात्रा 80% हो जाए, तो x का मान ज्ञात कीजिए?

A. 200
B. 220
C. 240
D. 270
E. 280

Option “C” is correct.

Turmeric = 64/100 * 300 = 192 gram

192 + x = 80/100 * (300 + x)

960 + 5x = 1200 + 4x

x = 240

179. A vessel contains 200 liters mixture of milk and water and contains 70% milk. If x liters of water is added to the mixture, so the ratio of milk to water in the final mixture becomes 7:5, find the value of x.

एक बर्तन में 200 लीटर दूध और पानी का मिश्रण है और इसमें 70% दूध है। यदि मिश्रण में x लीटर पानी मिलाया जाता है, तो अंतिम मिश्रण में दूध से पानी का अनुपात 7:5 हो जाता है, x का मान ज्ञात कीजिए।

A. 25
B. 40
C. 50
D. 100
E. None of these

Option “B” is correct.

Initial quantity of milk = 200 * 70/100 = 140 liters

Initial quantity of water = 200 – 140 = 60 liters

140/(60 + x) = 7/5

420 + 7x = 700

7x = 280

x = 40

180. A vessel contains 75 liters of a mixture of milk and water in the ratio of 4:1. If n liters of mixture is taken out and replaced by the same quantity of water and the same process is repeated one more time, then the quantity of milk left in the vessel is 38.4 liters. Find the value of n?

एक बर्तन में 4:1 के अनुपात में 75 लीटर दूध और पानी का मिश्रण है। यदि n लीटर मिश्रण को निकाल कर उतनी ही मात्रा में पानी डाल दिया जाए और उसी प्रक्रिया को एक बार फिर दोहराया जाए, तो बर्तन में बचे दूध की मात्रा 38.4 लीटर है। n का मान ज्ञात कीजिए?

A. 25
B. 15
C. 30
D. 10
E. None of these

Option “B” is correct.

The quantity of milk in the vessel initially = 75 * 4/(4 + 1) = 75 * 4/5 = 60 liters

60 * (1 – (n/75))2 = 38.4

(75 – n)2/752 = 38.4/60

(75 – n)2 = 38.4 * 752/60

75 – n = √3600

75 – n = 60

n = 75 – 60

n = 15

 

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